**Related Pages**

Rate, Time, Distance

Solving Speed, Time, Distance Problems Using Algebra

More Algebra Lessons

In these lessons, we will learn how to solve word problems involving average speed.

There are three main types of average problems commonly encountered in school algebra:

Average (Arithmetic Mean)

Weighted Average and

Average Speed.

The following diagram shows the formula for average speed. Scroll down the page for more examples and solutions on calculating the average speed.

**Example:**

John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour.
What was his average speed for the whole journey?

**Solution:**

Step 1: The formula for distance is

Distance = Rate × Time

Total distance = 50 × 3 + 60 × 2 = 270

Step 2: Total time = 3 + 2 = 5

Step 3: Using the formula:

**Answer:** The average speed is 54 miles per hour.

**Be careful!** You will get the wrong answer if you add
the two speeds and divide the answer by two.

How to calculate the average speed?

**Example:**

The speed paradox: If I drive from Oxford to Cambridge at 40 miles per hour and then from
Cambridge to Oxford at 60 miles per hour, what is my average speed for the whole journey?

**Example:**

On Alberto’s drive to his aunt’s house, the traffic was light, and he drove the 45-mile trip
in one hour. However, the return trip took his two hours. What was his average trip for the
round trip?

**Example:**

Mae took a non-stop flight to visit her grandmother. The 750-mile trip took three hours and
45 minutes. Because of the bad weather, the return trip took four hours and 45 minutes.
What was her average speed for the round trip?

If you are traveling in a car that travels 80km along a road in one hour, we say that you are traveling at an average of 80kn/h.

Average speed is the total distance divided by the total time for the trip. Therefore, speed is distance divided by time.

Instantaneous speed is the speed at which an object is traveling at any particular instant.

If the instantaneous speed of a car remains the same over a period of time, then we say that the car is traveling with constant speed.

The average speed of an object is the same as its instantaneous speed if that object is traveling at a constant speed.

**Example:**

Keri rollerblades to school, a total distance of 4.5km. She has to slow down twice to cross
busy streets, but overall the journey takes her 0.65h. What is Keri’s average speed during
the trip?

**Example:**

Elle drives 169 miles from Sheffield to London. Her average speed is 65 mph. She leaves
Sheffield at 6:30 a.m. Does she arrive in London by 9:00 a.m.?

**Example:**

Marie Ann is trying to predict the time required to ride her bike to the nearby beach. She
knows that the distance is 45 km and, from other trips, that she can usually average about
20 km/h. Predict how long the trip will take.

Try the free Mathway calculator and
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